1. (2 pts each) Consider the following algorithm: procedure polynomial(c, a0,a1,â€¦an: real numbers) powerâ‰”1 yâ‰”a0for i=1 to n Â Â powerâ‰”powercyâ‰”y+aipower return y (Note: y=ancn +...

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Advance Math

1. (2 pts each) Consider the following algorithm:
procedurepolynomial(c,a0,a1,â€¦an:real numbers)
powerâ‰”1
yâ‰”a₀for i=1 to n
Â Â powerâ‰”powerc*
*yâ‰”y+a_ipower
return** y
(Note: y=a_ncⁿ + a_n-1c^n-1 +. . . + a₁C +a₀ so the finalvalue of y is the value of the polynomial at x=c)
a. Use the algorithm to calculatef(3), wheref(x)=2x²+3x+1at x=3. Show the steps of working through the algorithm â€“donâ€™t just plug 3 in for x in f(x).
b. How many multiplications andadditions are needed to evaluate a polynomial of degree nat x=c?

Answer & Explanation Solved by verified expert

3.7 Ratings (399 Votes)

aWe have to calculate fx 2x2 3x1 at x 3So here we get a0 1 a1 3 a2 2 c 3From the algorithmStep 1Initialization Here we initialize the values as follows Step See Answer

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1. (2 pts each) Consider the following algorithm: procedure polynomial(c, a0,a1,â€¦an: real numbers) powerâ‰”1 yâ‰”a0for i=1 to n Â Â powerâ‰”power*cyâ‰”y+ai*power return y (Note: y=ancn +...